Problem: $z=-45i-15.5$ What are the real and imaginary parts of $z$ ? Choose 1 answer: Choose 1 answer: (Choice A) A $\text{Re}(z)=-15.5$ and $\text{Im}(z)=-45i$ (Choice B) B $\text{Re}(z)=-45$ and $\text{Im}(z)=-15.5$ (Choice C) C $\text{Re}(z)=-15.5$ and $\text{Im}(z)=-45$ (Choice D) D $\text{Re}(z)=-45i$ and $\text{Im}(z)=-15.5$
Solution: Background Complex numbers are numbers of the form $z={a}+{b}i$, where $i$ is the imaginary unit and ${a}$ and ${b}$ are real numbers. [What is the imaginary unit?] The real part of $z$ is denoted by $\text{Re}(z)={a}$. The imaginary part of $z$ is denoted by $\text{Im}(z)={b}.$ Finding the Real and Imaginary Parts of $z$ In this case, $z={-45}i-{15.5}$ is of the form ${b}i+{a}$, where ${a}={-15.5}$ and ${b}={-45}$. Therefore: $\text{Re}(z)={a}={-15.5}$. $\text{Im}(z)={b}={-45}$. Summary $\text{Re}(z)={-15.5}$ and $\text{Im}(z)={-45}$.